Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= 4 \\ -6x+y &= 6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = -y+6$ Divide both sides by $-6$ to isolate $x$ $x = {\dfrac{1}{6}y - 1}$ Substitute this expression for $x$ in the first equation. $-2({\dfrac{1}{6}y - 1}) - y = 4$ $-\dfrac{1}{3}y + 2 - y = 4$ Simplify by combining terms, then solve for $y$ $-\dfrac{4}{3}y + 2 = 4$ $-\dfrac{4}{3}y = 2$ $y = -\dfrac{3}{2}$ Substitute $-\dfrac{3}{2}$ for $y$ in the top equation. $-2x+ \dfrac{3}{2} = 4$ $-2x+\dfrac{3}{2} = 4$ $-2x = \dfrac{5}{2}$ $x = -\dfrac{5}{4}$ The solution is $\enspace x = -\dfrac{5}{4}, \enspace y = -\dfrac{3}{2}$.